The ANO (CAP 393) defines cross country a mentioned above (3 nm from aerodrom of departure). It is in Schedule 8, Part B.
Then try placing this in the correct context
5. For the purposes of this Section—
“Cross-country flight” means any flight during the course of which the aircraft is more than three nautical miles from the aerodrome of departure.
and
This Section (ANO Schedule 7 PART B Ratings and qualifications SECTION 1) is all about the privileges of instructors
Restrictions - restricted privileges
(3) The privileges are restricted to carrying out under the supervision of the holder of a flight instructor rating approved for this purpose—
(a) flight instruction for the issue of the Private Pilot Licence or those parts of integrated courses at Private Pilot Licence level and type ratings for single engine aeroplanes, excluding approval of first solo flights by day or by night and first solo cross-country flights by day or by night
Thus, this definition is only relevant to defining cross country for the purpose of the "Restriction" in a FI rating, and has nothing to do with defining cross country flight requirements for the purpose of qualifying for licence issue.
EASA Part FCL defines Cross Country as:
Cross-Country.
A flight between a point of departure and a point of arrival following a pre –planned route using standard navigation procedures.